I have used the successive convex approximation to transform the problem into a convex optimization problem, but there is still something wrong when solving the problem by CVX with MOSEK. Message of CVX is as follows:

## Calling Mosek 9.1.9: 3900 variables, 1802 equality constraints

MOSEK Version 9.1.9 (Build date: 2019-11-21 11:34:40)

Copyright © MOSEK ApS, Denmark. WWW: mosek.com

Platform: Windows/64-X86

Problem

Name :

Objective sense : min

Type : CONIC (conic optimization problem)

Constraints : 1802

Cones : 800

Scalar variables : 3900

Matrix variables : 0

Integer variables : 0

Optimizer started.

Presolve started.

Eliminator - tries : 0 time : 0.00

Lin. dep. - tries : 0 time : 0.00

Lin. dep. - number : 0

Presolve terminated. Time: 0.00

Optimizer terminated. Time: 0.05

Interior-point solution summary

Problem status : DUAL_INFEASIBLE

Solution status : DUAL_INFEASIBLE_CER

Primal. obj: -1.0873703084e-08 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 cones: 0e+00

Optimizer summary

Optimizer - time: 0.05

Interior-point - iterations : 0 time: 0.01

Basis identification - time: 0.00

Primal - iterations : 0 time: 0.00

Dual - iterations : 0 time: 0.00

Clean primal - iterations : 0 time: 0.00

Clean dual - iterations : 0 time: 0.00

Simplex - time: 0.00

Primal simplex - iterations : 0 time: 0.00

Dual simplex - iterations : 0 time: 0.00

Mixed integer - relaxations: 0 time: 0.00

Status: Unbounded

Optimal value (cvx_optval): +Inf

Is CVX unable to solve this problem? My code is as follows:

cvx_begin

cvx_solver mosek

variable traj(para.T+1, 2)

variable u(1, para.T)

variable v(1, para.T)

variable t(1, para.T)

expression lower_bound(1, para.T)

expression D(1, para.T)

for ii=1:para.T

lower_bound(ii) = coe3(ii)*u(ii) + coe4(ii)*v(ii);

D(ii)= coe5(ii)*t(ii) + coe6(ii)*v(ii);

end

maximize(1/para.T*(sum((lower_bound)-D)))

subject to

80 <= u;

40 <= v;

80 <= t;

for jj=1:para.T

pow_pos(norm(traj(jj, :)-para.place_u(1:2)),2)+6400+u0(jj)^2-2*u0(jj)*u(jj)<=0;
pow_pos(norm(traj(jj, :)-para.place_R(1:2)),2)+1600+v0(jj)^2-2*v0(jj)

*v(jj)<=0;*

pow_pos(norm(traj(jj, :)-para.place_e(1:2)),2)+6400+t0(jj)^2-2t0(jj)*t(jj)<=0;

pow_pos(norm(traj(jj, :)-para.place_e(1:2)),2)+6400+t0(jj)^2-2

end

for ii=1:para.T

pow_pos(norm(traj(ii+1,:)-traj(ii, :)),2)<=para.Vmax^2;

end

cvx_end

Thanks for your help.